Question

Need help with finding the following with the given equation.

y = 2x^2 - 12x + 7

1. Find the X and Y values
2. Find the axis of symmetry
3. Use the quadratic formula to find the two solutions to X (y=0)
4. Find the discriminant

Answer 1

Let's answer question 3 first, because by solving it through the quadratic formula, we actually get the discriminant for free and it's easy to get the axis of symmetry.

In this quadratic, 2x²- 12x + 7 the values for the quadratic formula are a = 2, b = -12, c = 7. (Read the coefficients with a for the squared term, b for the x term, c for the number).

The axis of symmetry is at x =
`(-b)/(2a) = (-(-12))/(2*2) = 3`

Remember that
`(-b)/(2a)` part? That's half of the quadratic formula.

x =
`x = \frac{-b + \sqrt{b^(2)-4ac}}{2a} or x = \frac{-b - \sqrt{b^(2)-4ac}}{2a}`

(You often see the plus or minus part, but this chat box doesn't have that key.) Also, the discriminant is the other half - the b²-4ac part. That is 12²-4(2)(7) = 144 - 56 = 88.

`x = \frac{-(-12) + \sqrt{((-12)^(2)-4(2)(7))}}{2(2)} or x = \frac{-(-12) - \sqrt{((-12)^(2)-4(2)(7)})}{2(2)}`

`x = (12 + √(144-56))/(4) or x = (12 - √(144-56))/(4)`

`x = (12+√(88))/(4) or x = (12-√(88))/(4)`

`x = (12 + √(4)√(22))/(4) or x = (12 - √(4)√(22))/(4)`

`x = (12+ 2√(22))/(4) or x = (12- 2√(22))/(4)`

`x = (6+√(22))/(2) or x = (6-√(22))/(2)`

Thus,
`x = (6+√(22))/(2) or x = (6-√(22))/(2)` are the solutions, the axis of symmetry is at x =3, and the discriminant is 88.